Answer:
The factors are \((x-7)\) and \((x+2)\)
Step-by-step explanation:
we have
\(x^{2} -5x-14\)
To find the factors equate the equation to zero
\(x^{2} -5x-14=0\)
Group terms that contain the same variable, and move the constant to the opposite side of the equation
\(x^{2} -5x=14\)
Complete the square. Remember to balance the equation by adding the same constants to each side
\(x^{2} -5x+6.25=14+6.25\)
\(x^{2} -5x+6.25=20.25\)
Rewrite as perfect squares
\((x-2.5)^{2}=20.25\)
\((x-2.5)=(+/-)\sqrt{20.25}\)
\((x-2.5)=(+/-)4.5\)
\(x=2.5(+/-)4.5\)
\(x=2.5+4.5=7\)
\(x=2.5-4.5=-2\)
therefore
\(x^{2} -5x-14=(x-7)(x+2)\)
using a graphing tool see the attached figure
The factors of the quadratic equation are the x-intercepts (values of x when the value of the function is equal to zero)
